Subgroups — C₂×C₁₃×#3220 #15747130

Order 3328.

2342 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3220	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
18	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
19	C₁₃×#540	—	2	4	no	—
20	C₁₃×#540	C₂²	1	8	yes	complemented
21	C₁₃×#535	—	2	4	no	—
22	C₁₃×#535	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#123	—	2	2	no	—
30	C₂×C₁₃×#121	—	2	2	no	—
31	C₂×C₁₃×#121	—	2	2	no	—
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₂×C₁₃×#120	—	2	2	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#496	C₂²	1	8	yes	complemented
37	C₁₃×#493	C₂²	1	8	yes	complemented
38	C₁₃×#490	C₂²	1	8	yes	complemented
39	C₁₃×#488	C₂²	1	8	yes	complemented
40	C₁₃×#463	C₂²	1	16	yes	complemented
41	C₁₃×#459	C₂²	1	16	yes	complemented
42	C₁₃×#449	C₂²	1	16	yes	complemented
43	C₁₃×#447	C₂²	1	16	yes	complemented
44	C₁₃×#433	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₂×C₁₃×#102	C₂²	1	2	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₁₃	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	4	4	no	—
56	C₂×C₁₃×#41	C₂³	1	4	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	4	4	no	—
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	—	2	2	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×SD₁₆	—	4	4	no	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
76	C₂×C₁₃×D₈	—	4	4	no	—
77	C₂×C₁₃×D₈	—	4	4	no	—
78	C₂×C₁₃×D₈	—	4	4	no	—
79	C₂×C₁₃×D₈	C₂³	1	8	yes	—
80	C₂×C₁₃×D₈	C₂³	1	8	yes	—
81	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#127	C₂³	1	4	yes	—
88	C₁₃×#127	C₂³	1	4	yes	—
89	C₁₃×#127	C₂³	1	4	yes	complemented
90	C₁₃×#125	—	2	2	no	—
91	C₁₃×#125	C₂³	1	4	yes	complemented
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×#124	C₂³	1	4	yes	—
96	C₁₃×#123	—	2	16	no	—
97	C₁₃×#121	—	2	4	no	—
98	C₁₃×#121	—	2	16	no	—
99	C₁₃×#121	—	2	16	no	—
100	C₁₃×#121	C₂³	1	8	yes	—
101	C₁₃×#120	—	2	16	no	—
102	C₄×D₄×C₁₃	—	2	4	no	—
103	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
104	C₁₃×#117	D₄	1	4	yes	—
105	C₁₃×#117	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
117	C₁₃×#103	C₂³	1	8	yes	complemented
118	C₁₃×#102	C₂³	1	8	yes	—
119	C₁₃×#102	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	8	yes	complemented
121	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#97	C₂³	1	4	yes	complemented
123	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
124	C₂×#3220	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	2	no	—
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	1	no	—
129	C₂⁴×C₁₃	—	2	4	no	—
130	C₂⁴×C₁₃	—	4	4	no	—
131	C₂⁴×C₁₃	—	8	4	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₁₃×#41	—	4	8	no	—
134	C₁₃×#41	—	4	8	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	4	no	—
157	C₂×D₄×C₁₃	—	8	4	no	—
158	C₂×D₄×C₁₃	—	8	4	no	—
159	C₂×D₄×C₁₃	—	8	4	no	—
160	C₂×D₄×C₁₃	—	8	4	no	—
161	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	—	8	4	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×SD₁₆	—	4	8	no	—
179	C₁₃×D₈	—	4	8	no	—
180	C₁₃×D₈	—	4	8	no	—
181	C₁₃×D₈	—	4	8	no	—
182	C₂×C₈×C₁₃	—	2	4	no	—
183	C₂×C₈×C₁₃	—	2	4	no	—
184	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	—	2	8	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₄²×C₁₃	C₂⁴	1	2	yes	—
198	C₄²×C₁₃	C₂⁴	1	2	yes	—
199	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#3220	C₂×C₁₃	1	16	yes	direct product factor
202	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#463	C₂×C₁₃	1	2	yes	complemented
207	C₂×#459	C₂×C₁₃	1	2	yes	complemented
208	C₂×#449	C₂×C₁₃	1	2	yes	complemented
209	C₂×#447	C₂×C₁₃	1	2	yes	complemented
210	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	4	8	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	4	2	no	—
221	C₂³×C₁₃	—	4	4	no	—
222	C₂³×C₁₃	—	4	4	no	—
223	C₂³×C₁₃	—	4	4	no	—
224	C₂³×C₁₃	—	4	4	no	—
225	C₂³×C₁₃	—	4	4	no	—
226	C₂³×C₁₃	—	4	4	no	—
227	C₂³×C₁₃	—	8	8	no	—
228	C₂³×C₁₃	—	8	16	no	—
229	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	2	4	no	—
234	D₄×C₁₃	—	2	4	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	8	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	8	8	no	—
245	D₄×C₁₃	—	8	8	no	—
246	D₄×C₁₃	—	8	8	no	—
247	D₄×C₁₃	—	8	8	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	4	8	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	8	8	no	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
264	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
265	C₈×C₁₃	—	2	4	no	—
266	C₈×C₁₃	—	2	4	no	—
267	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
268	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
270	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
271	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
272	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
273	#540	—	2	4	no	—
274	#540	C₂²×C₁₃	1	8	yes	complemented
275	#535	—	2	4	no	—
276	#535	C₂²×C₁₃	1	8	yes	complemented
277	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#123	—	2	2	no	—
284	C₂×#121	—	2	2	no	—
285	C₂×#121	—	2	2	no	—
286	C₂×#121	C₂²×C₁₃	1	2	yes	—
287	C₂×#120	—	2	2	no	—
288	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
289	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
290	#496	C₂²×C₁₃	1	8	yes	complemented
291	#493	C₂²×C₁₃	1	8	yes	complemented
292	#490	C₂²×C₁₃	1	8	yes	complemented
293	#488	C₂²×C₁₃	1	8	yes	complemented
294	#463	C₂²×C₁₃	1	16	yes	complemented
295	#459	C₂²×C₁₃	1	16	yes	complemented
296	#449	C₂²×C₁₃	1	16	yes	complemented
297	#447	C₂²×C₁₃	1	16	yes	complemented
298	#433	C₂²×C₁₃	1	8	yes	complemented
299	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
300	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
301	C₂×#102	C₂²×C₁₃	1	2	yes	—
302	C₂×#102	C₂²×C₁₃	1	2	yes	—
303	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
304	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
305	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
306	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	2	4	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	4	4	no	—
315	C₂²×C₁₃	—	4	4	no	—
316	C₂²×C₁₃	—	4	4	no	—
317	C₂²×C₁₃	—	4	4	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	8	16	no	—
320	C₂²×C₁₃	—	8	4	no	—
321	C₂²×C₁₃	—	8	8	no	—
322	C₂²×C₁₃	—	8	4	no	—
323	C₂²×C₁₃	—	8	4	no	—
324	C₂²×C₁₃	#535	1	2	yes	—
325	C₂²×C₁₃	#576	1	4	yes	—
326	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	4	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	#535	1	2	yes	—
333	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂⁵	—	2	1	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	4	4	no	—
337	C₂×#41	C₂³×C₁₃	1	4	yes	—
338	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	4	4	no	—
347	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
348	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	2	no	—
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×SD₁₆	—	4	4	no	—
356	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
357	C₂×D₈	—	4	4	no	—
358	C₂×D₈	—	4	4	no	—
359	C₂×D₈	—	4	4	no	—
360	C₂×D₈	C₂³×C₁₃	1	8	yes	—
361	C₂×D₈	C₂³×C₁₃	1	8	yes	—
362	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
363	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
364	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
365	#127	—	2	2	no	—
366	#127	—	2	2	no	—
367	#127	—	2	2	no	—
368	#127	C₂³×C₁₃	1	4	yes	—
369	#127	C₂³×C₁₃	1	4	yes	—
370	#127	C₂³×C₁₃	1	4	yes	complemented
371	#125	—	2	2	no	—
372	#125	C₂³×C₁₃	1	4	yes	complemented
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	C₂³×C₁₃	1	4	yes	—
376	#124	C₂³×C₁₃	1	4	yes	—
377	#123	—	2	16	no	—
378	#121	—	2	4	no	—
379	#121	—	2	16	no	—
380	#121	—	2	16	no	—
381	#121	C₂³×C₁₃	1	8	yes	—
382	#120	—	2	16	no	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
385	#117	D₄×C₁₃	1	4	yes	—
386	#117	C₂³×C₁₃	1	4	yes	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
398	#103	C₂³×C₁₃	1	8	yes	complemented
399	#102	C₂³×C₁₃	1	8	yes	—
400	#102	C₂³×C₁₃	1	8	yes	—
401	#102	C₂³×C₁₃	1	8	yes	complemented
402	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
403	#97	C₂³×C₁₃	1	4	yes	complemented
404	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
405	C₂×C₁₃	—	4	2	no	—
406	C₂×C₁₃	—	8	2	no	—
407	C₂×C₁₃	—	8	4	no	—
408	C₂×C₁₃	—	8	2	no	—
409	C₂×C₁₃	—	8	2	no	—
410	C₂×C₁₃	#3220	1	4	yes	direct product factor
411	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#576	1	2	yes	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	—	2	1	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	4	4	no	—
419	C₂⁴	—	8	4	no	—
420	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
421	#41	—	4	8	no	—
422	#41	—	4	8	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	8	4	no	—
446	C₂×D₄	—	8	4	no	—
447	C₂×D₄	—	8	4	no	—
448	C₂×D₄	—	8	4	no	—
449	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
450	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
451	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
452	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	8	4	no	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
466	SD₁₆	—	4	8	no	—
467	D₈	—	4	8	no	—
468	D₈	—	4	8	no	—
469	D₈	—	4	8	no	—
470	C₂×C₈	—	2	4	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
477	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
483	C₄²	C₂×D₄×C₁₃	1	2	yes	—
484	C₄²	C₂×D₄×C₁₃	1	2	yes	—
485	C₄²	C₂⁴×C₁₃	1	2	yes	—
486	C₄²	C₂⁴×C₁₃	1	2	yes	—
487	C₁₃	C₂×#3220	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	8	8	no	—
505	C₂³	—	8	16	no	—
506	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
507	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	Q₈	—	2	4	no	—
509	Q₈	—	4	2	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	8	8	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	8	no	—
524	D₄	—	8	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	8	8	no	—
536	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
541	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	16	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	8	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	C₁₃×#535	1	2	yes	—
562	C₂²	C₁₃×#576	1	4	yes	—
563	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	2	no	—
569	C₄	C₁₃×#535	1	2	yes	—
570	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	2	no	—
574	C₂	—	8	4	no	—
575	C₂	—	8	2	no	—
576	C₂	C₁₃×#3220	1	4	yes	direct product factor
577	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
578	C₂	C₂×C₁₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₃×#540	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3220	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#493	C₂	semidirect
6. C₂×C₁₃×#490	C₂	semidirect
7. C₂×C₁₃×#488	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
9. C₂×C₁₃×#459	C₂	semidirect
10. C₂×C₁₃×#449	C₂	semidirect
11. C₂×C₁₃×#447	C₂	semidirect
12. C₂×C₁₃×#433	C₂	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
18. C₂²×C₁₃×D₈	C₂²	semidirect
20. C₁₃×#540	C₂²	semidirect
22. C₁₃×#535	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
26. C₂×C₁₃×#125	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₁₃×#496	C₂²	semidirect
37. C₁₃×#493	C₂²	semidirect
38. C₁₃×#490	C₂²	semidirect
39. C₁₃×#488	C₂²	semidirect
40. C₁₃×#463	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#449	C₂²	semidirect
43. C₁₃×#447	C₂²	semidirect
44. C₁₃×#433	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
46. C₂×C₁₃×#103	C₂²	semidirect
49. C₂×C₁₃×#102	C₂²	semidirect
51. C₂×C₁₃×#97	C₂²	semidirect
52. C₂×C₄×C₈×C₁₃	C₂²	semidirect
75. C₂×C₁₃×SD₁₆	C₂³	semidirect
81. C₂×C₁₃×D₈	C₂³	semidirect
89. C₁₃×#127	C₂³	semidirect
91. C₁₃×#125	C₂³	semidirect
103. C₄×D₄×C₁₃	C₂³	semidirect
116. C₁₃×C₄⋊C₈	C₂³	semidirect
117. C₁₃×#103	C₂³	semidirect
120. C₁₃×#102	C₂³	semidirect
122. C₁₃×#97	C₂³	semidirect
123. C₄×C₈×C₁₃	C₂³	semidirect
124. C₂×#3220	C₁₃	direct (N × H)
199. C₂×#540	C₂×C₁₃	semidirect
200. C₂×#535	C₂×C₁₃	semidirect
201. #3220	C₂×C₁₃	direct (N × H)
202. C₂×#496	C₂×C₁₃	semidirect
203. C₂×#493	C₂×C₁₃	semidirect
204. C₂×#490	C₂×C₁₃	semidirect
205. C₂×#488	C₂×C₁₃	semidirect
206. C₂×#463	C₂×C₁₃	semidirect
207. C₂×#459	C₂×C₁₃	semidirect
208. C₂×#449	C₂×C₁₃	semidirect
209. C₂×#447	C₂×C₁₃	semidirect
210. C₂×#433	C₂×C₁₃	semidirect
269. C₂²×SD₁₆	C₂²×C₁₃	semidirect
272. C₂²×D₈	C₂²×C₁₃	semidirect
274. #540	C₂²×C₁₃	semidirect
276. #535	C₂²×C₁₃	semidirect
279. C₂×#127	C₂²×C₁₃	semidirect
280. C₂×#125	C₂²×C₁₃	semidirect
288. C₂×C₄×D₄	C₂²×C₁₃	semidirect
290. #496	C₂²×C₁₃	semidirect
291. #493	C₂²×C₁₃	semidirect
292. #490	C₂²×C₁₃	semidirect
293. #488	C₂²×C₁₃	semidirect
294. #463	C₂²×C₁₃	semidirect
295. #459	C₂²×C₁₃	semidirect
296. #449	C₂²×C₁₃	semidirect
297. #447	C₂²×C₁₃	semidirect
298. #433	C₂²×C₁₃	semidirect
299. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
300. C₂×#103	C₂²×C₁₃	semidirect
303. C₂×#102	C₂²×C₁₃	semidirect
305. C₂×#97	C₂²×C₁₃	semidirect
306. C₂×C₄×C₈	C₂²×C₁₃	semidirect
356. C₂×SD₁₆	C₂³×C₁₃	semidirect
362. C₂×D₈	C₂³×C₁₃	semidirect
370. #127	C₂³×C₁₃	semidirect
372. #125	C₂³×C₁₃	semidirect
384. C₄×D₄	C₂³×C₁₃	semidirect
397. C₄⋊C₈	C₂³×C₁₃	semidirect
398. #103	C₂³×C₁₃	semidirect
401. #102	C₂³×C₁₃	semidirect
403. #97	C₂³×C₁₃	semidirect
404. C₄×C₈	C₂³×C₁₃	semidirect
410. C₂×C₁₃	#3220	direct (N × H)
487. C₁₃	C₂×#3220	direct (N × H)
576. C₂	C₁₃×#3220	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#540	2
C₂×C₁₃×#535	2
C₁₃×#3220	2
C₂×C₁₃×#496	2
C₂×C₁₃×#493	2
C₂×C₁₃×#490	2
C₂×C₁₃×#488	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#449	2
C₂×C₁₃×#447	2
C₂×C₁₃×#433	2
C₂×#3220	13

Subgroups — C2×C13×#3220 #15747130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3220 #15747130